1. Field of the Invention
The invention relates to a digital filter arrangement for filtering non-uniformly quantitised pulse code-modulated signals formed by a succession of code groups x(i) each comprising a segment number s(i) and a mantissa number m(i).
2. Description of the Prior Art
As known non-uniform pulse code-modulation enables the conversion of information signals, which vary over a large dynamic range, into code groups whose number of bits is smaller than the number of bits from which the numbers should consist which would be obtained by uniform pulse code-modulation. The result is that when using non-uniform pulse code-modulation, the bit rate on the transmission path is lower than with uniform pulse code-modulation and that the signal-to-quantising noise ratio over a considerable portion of the dynamic range is constant.
A non-uniformly quantised pulse code-modulated signal is obtained by performing a non-linear processing on the information signal. This non-linear processing operation is known as compression. The characteristic indicating the relationship between the information signal and the non-uniformly pulse code-modulated signal is called the compression characteristic. The most customary compression characteristics are the 13-segment A-law and the 15-segment .mu.-law characteristics.
The segment number s(i) in the code group x(i) now indicates, in base-2-code, the segments number. This number s(i) comprises N.sub.1 bits which are called the characteristic bits. If, for the compression, use is made of one of the two above-defined compression characteristics, then N.sub.1 =3 and the binary coded segment number is equal to s.sub.2 s.sub.1 s.sub.0, wherein s.sub.0 represents the least significant and s.sub.2 the most significant bit and wherein s.sub.j is equal to 1 or 0.
The mantissa number m(i) in the code group x(i) indicates, in base-2-code, the number of quantising steps on the segment s(i). This number m(i) comprises N.sub.2 bits which are called the mantissa bits. When using the above defined compression characteristics, N.sub.2 is equal to 4. The number m(i) is now given by e.sub.3 e.sub.2 e.sub.1 e.sub.0. Also here it holds that e.sub.0 is the least significant and e.sub.3 the most significant bit and that e.sub.j has the value 1 or 0.
As known (see for example reference 2), filtering a digital signal formed by a sequence of numbers z(i) means that a sequence of numbers y(i) must be determined, the relationship between y(i) and z(i) being given by the expression ##EQU1## if a non-recursive digital filter is used. In (1), a(k) represents a weighting factor which is called the filter coefficient.
If a recursive digital filter is used for filtering a digital signal, the relationship between y(i) and z(i) is given by the expression: ##EQU2## In (2) a(k) and b(k) again represent filter coefficients.
If now a non-uniformly quantised pulse code-modulated signal is applied to the digital filter, in order that a useful result may be obtained, to first convert this signal into a uniformly quantised pulse code-modulated signal formed by a sequence of numbers z(i) each related in a manner still to be described (see also reference 1) to the numbers s(i) and m(i).
When designing a digital filter, there are two parameters which have an extremely important influence on the ultimate implementation. First, there is the required storage capacity and second, the maximum permissible internal processing rate.
For a non-recursive digital filter (see expression 1), the required storage capacity is determined by the value of N and the number of bits of the numbers a(k) and z(j). For a recursive digital filter (see expression 2), the required storage capacity is, in addition, determined by the value M and the number of bits of the numbers b(k) and y(i).
The internal processing rate is inter alia determined by the number of bits of the numbers a(k), b(k), z(i) and y(i).
Since, in general, a number s(i) in the uniformly quantised pulse code-modulated signal will comprise a greater number of bits than a code group x(i) in the non-uniformly quantised pulse code-modulated signal, it is advantageous to store the code groups x(i), as described in reference 3, instead of the numbers z(i).
The non-recursive digital filter, described in reference 3, for non-uniformly quantised pulse code-modulated signals, is constituted more in particular by a cascade arrangement of N storage sections, each arranged for storing and supplying a code group x(i). The output of each of the storage sections is connected to an adding arrangement through a branch in which a storage medium is incorporated. The products of all possible values of z(i) and the filter coefficients a(k), characteristic for the relevant branch, are stored in each of these storage media. If it is now assumed that the products a(k), z(i-k), stored in the storage media, consist of thirteen bits, the storage capacity of each storage medium must be 13.times.2.sup.8 so that a total storage capacity of 8 N+13.times.2.sup.8 .times.N bits is required in this digital filter. Since the product of a(k) and z(i-k) has been stored in the storage medium, the internal processing rate may be low since now only N adding operations need be performed. In contradistinction therewith is the enormously large storage capacity required, amounting to some hundreds of thousands of bits for normal values of N (for example N=100).